Yes, it's alert-style notifications — after returning from display sleep (and, when do-not-disturb is turned off).
(Alert-style notifications stay on the screen until you dismiss them.)
This motion behavior of alert-style notifications is very distracting — and there is no setting by which to turn it off. macOS Ventura 13.7.8
Here's a flow of events:
1 Desktop is stable.
2 An [alert] notification is displaying in upper right corner.
3 Hot Corner shortcut of "Put Display To Sleep" is actuated.
4 Screen goes black.
5 Mouse clicked.
6 Screen lights up — but the notification is not showing.
7 Instantly, the notification appears in the lower right corner,
and zips up the right side of the screen.
8 That [alert] notification is displaying in upper right corner.
9 Desktop is stable.
A video recording of the reappearing notifications, sliding up the side of the screen, after returning from display sleep. (Mute the annoying, irrelevant sound.)
https://youtube.com/shorts/H5omC7n04Ys